# zlasr (l) - Linux Manuals

## NAME

ZLASR - applies a sequence of real plane rotations to a complex matrix A, from either the left or the right

## SYNOPSIS

SUBROUTINE ZLASR(
SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )

CHARACTER DIRECT, PIVOT, SIDE

INTEGER LDA, M, N

DOUBLE PRECISION C( * ), S( * )

COMPLEX*16 A( LDA, * )

## PURPOSE

ZLASR applies a sequence of real plane rotations to a complex matrix A, from either the left or the right. When SIDE = aqLaq, the transformation takes the form

A := P*A
and when SIDE = aqRaq, the transformation takes the form

A := A*P**T
where P is an orthogonal matrix consisting of a sequence of z plane rotations, with z = M when SIDE = aqLaq and z = N when SIDE = aqRaq, and P**T is the transpose of P.

When DIRECT = aqFaq (Forward sequence), then

P(z-1) ... P(2) P(1)

and when DIRECT = aqBaq (Backward sequence), then

P(1) P(2) ... P(z-1)

where P(k) is a plane rotation matrix defined by the 2-by-2 rotation

R(k)  c(k)  s(k) )

-s(k)  c(k) ).

When PIVOT = aqVaq (Variable pivot), the rotation is performed for the plane (k,k+1), i.e., P(k) has the form

P(k)                                             )
...                                     )
)
c(k)  s(k)                  )
-s(k)  c(k)                  )
)
...       )
)
where R(k) appears as a rank-2 modification to the identity matrix in rows and columns k and k+1.

When PIVOT = aqTaq (Top pivot), the rotation is performed for the plane (1,k+1), so P(k) has the form

P(k)  c(k)                    s(k)                 )
)
...                              )
)
-s(k)                    c(k)                 )
)
...      )
)
where R(k) appears in rows and columns 1 and k+1.

Similarly, when PIVOT = aqBaq (Bottom pivot), the rotation is performed for the plane (k,z), giving P(k) the form

P(k)                                             )
...                                      )
)
c(k)                    s(k) )
)
...              )
)
-s(k)                    c(k) )
where R(k) appears in rows and columns k and z. The rotations are performed without ever forming P(k) explicitly.

## ARGUMENTS

SIDE (input) CHARACTER*1
Specifies whether the plane rotation matrix P is applied to A on the left or the right. = aqLaq: Left, compute A := P*A
= aqRaq: Right, compute A:= A*P**T
PIVOT (input) CHARACTER*1
Specifies the plane for which P(k) is a plane rotation matrix. = aqVaq: Variable pivot, the plane (k,k+1)
= aqTaq: Top pivot, the plane (1,k+1)
= aqBaq: Bottom pivot, the plane (k,z)
DIRECT (input) CHARACTER*1
Specifies whether P is a forward or backward sequence of plane rotations. = aqFaq: Forward, P = P(z-1)*...*P(2)*P(1)
= aqBaq: Backward, P = P(1)*P(2)*...*P(z-1)
M (input) INTEGER
The number of rows of the matrix A. If m <= 1, an immediate return is effected.
N (input) INTEGER
The number of columns of the matrix A. If n <= 1, an immediate return is effected.
C (input) DOUBLE PRECISION array, dimension
(M-1) if SIDE = aqLaq (N-1) if SIDE = aqRaq The cosines c(k) of the plane rotations.
S (input) DOUBLE PRECISION array, dimension
(M-1) if SIDE = aqLaq (N-1) if SIDE = aqRaq The sines s(k) of the plane rotations. The 2-by-2 plane rotation part of the matrix P(k), R(k), has the form R(k) = ( c(k) s(k) ) ( -s(k) c(k) ).
A (input/output) COMPLEX*16 array, dimension (LDA,N)
The M-by-N matrix A. On exit, A is overwritten by P*A if SIDE = aqRaq or by A*P**T if SIDE = aqLaq.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).